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A structural study of very high-density amorphous ice
Chemical Physics Letters 397 (2004) 335–339 www.elsevier.com/locate/cplett
A structural study of very high-density amorphous ice Malcolm Guthrie a
a,b
, Chris A. Tulk
a,*
, Chris J. Benmore b, Dennis D. Klug
c
Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA b Argonne National Laboratory, Argonne, IL 60439, USA c National Research Council of Canada, Ottawa, Ontano, Canada K0A 0R6 Received 8 July 2004 Available online 25 September 2004
Abstract Neutron and X-ray structure factor functions of very high-density amorphous (VHDA) ice have been measured and compared with those of the high- and low-density amorphous forms. The principal peak in the VHDA structure factor is sharper than that ˚ , close to 2.85 A ˚ observed in the HDA ice form. Radial distribution functions (rdfs) indicate the local O O separation is 2.83 A estimated from earlier Raman measurements, but larger than that observed by empirical potential structure refinement simulation of neutron data. Perhaps more importantly the rdfs indicate a greater extent of ordering in VHDA ice, with observable coordination ˚. shells extending to at least 20 A 2004 Elsevier B.V. All rights reserved.
Since the discovery of pressure-amorphised ice 20 years ago [1], the structures of the high-density amorphous (HDA) and low-density amorphous (LDA) ice forms [1–3], and their relation to liquid water have been the subject of intense discussion [4] and by now the basic structural features of each form are well understood. Quite recently however there has been increasing interest in a higher-density form that is synthesized by annealing the HDA form isothermally under pressure [5–7]. Details of the structure of this very high-density form and the relation to HDA and LDA are of current interest, particularly since annealing the amorphous form under pressure is a common practice when forming highdensity pressure amorphized ice and studying the transformation process to the lower density form. Additionally, it has been suggested that the very high-density amorphous (VHDA) ice form may be related to the high-temperature liquid. Understanding the subtle effects of synthesis conditions on the resulting structure may help in understanding the high–low-density amor*
Corresponding author. E-mail address: [email protected] (C.A. Tulk).
0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.07.116
phous ice transformation process. Furthermore, many in situ experiments are preformed at elevated temperatures where the production of this VHDA ice form may be more likely than those formed at liquid nitrogen temperature [4,8,9]. The initial report of the VHDA ice included Raman spectroscopic and some X-ray measurements, but the X-ray data could not be analysed to provide detailed structural information. Subsequently, VHDA ice has been studied using an empirical potential structure refinement (EPSR) technique applied to neutron diffraction data [6]. While these characterisations have shed light onto the structure of VHDA ice, the precise value of the nearest-neighbour O O distance is inconsistent and remains unclear. This may be a result of the weak contribution of the O–O partial to the total neutron S(Q). The Raman data implies a longer bond length than the EPSR simulation. Due to the relative scattering power of waterÕs hydrogen and oxygen atoms the total X-ray structure factor is dominated by the O–O partial [10,11], where as in the case of neutron scattering the O–O partial contributes to less than 9% of the total scattering. This greater
336
M. Guthrie et al. / Chemical Physics Letters 397 (2004) 335–339
sensitivity to the O–O partial is especially important, since it shows the most pronounced differences among the various amorphous ice forms [12,2]. In the work presented here both the neutron and X-ray structure factors S(Q) have been measured, and this data is used to discuss both the local structure and intermediate-range ordering of the VHDA form. We note that, the intermediate-range structure, which may play a significant role in the transformation processes, has not been commented on previously in any great detail. In particular, we compare the VHDA structure to both the lowdensity and high-density structures. The form of the structure factor, S(Q) for both neutron and X-ray diffraction are given below as (the subscript n refers to neutron terms and the subscript x refers to X-ray terms): ( ), !2 X X 2 S n ðQÞ ¼ I n ðQÞ ca ba P ðQÞ c a ba ; a
indium vessel inside a piston-cylinder pressure cell, and cooled to 77 K by immersion in liquid-nitrogen. Both the sample and indium container were then pressurised to 1.8 GPa, followed by depressurization to 1.25 GPa where the sample was warmed from 77 to 165 K, as determined by the average reading of thermocouples attached to the top and bottom of the pressure cell cylinder. These conditions were maintained for 15 min. The sample was then cooled to 77 K and the pressure gradually released to zero. The volume of the sample was estimated from the length of the indium tube at ambient pressure and was found to be 10 ± 2% smaller than the average found for HDA ice prepared in a similar manner, but without the annealing process. The indium canister containing the VHDA sample was recovered under liquid nitrogen, and transferred directly to a storage dewar for shipping to the Argonne National Laboratory (ANL) for the subsequent study. For the neutron scattering experiment the sample was extracted from the indium container and 1 cm3 was placed in a vanadium canister under liquid nitrogen (a smaller amount was kept in reserve, also under liquid nitrogen, for the X-ray measurement). The vanadium canister was then transferred to a continuous-flow Oxford He cryostat mounted in the SEPD instrument at the Intense Pulsed Neutron Source, ANL. The cryostat had been pre-cooled to 40 K and the temperature during the transfer to the cryostat did not exceed 77 K. After the sample loading was complete, the temperature was gradually raised to 80 K to boil off any remaining nitrogen, before being lowered to 40 K and data collected. Standard corrections including subtraction of the container scattering, absorption, multiple-scattering effects and inelastic scattering were implemented using the software package PDFGETN [14]. The resulting neutron Sn(Q) function is shown in Fig. 1a, along with that measured previously from HDA and LDA [15].
a
ð1Þ S x ðQÞ ¼
fI x ðQÞ hF 2 i CðQÞg hF i2
ð2Þ
:
In these equations, I(Q) is the corrected measured intensity. The individual atoms within a given molecule of the sample material are labeled a, and ca represents the fractional proportion of atoms of type a, for neutrons ba are the neutron scattering length of atom type a, and P(Q) is the inelastic (Plazeck) contribution. For X-rays ÆF2æ represents the average scattering from an independent molecule and C(Q) is the Compton scattering contribution [13]. A sample of VHDA ice (99.979% D2O by weight, purchased from Atomic Energy of Canada Ltd.) was prepared at the National Research Council of Canada. Approximately 2.2 cm3 of water were loaded into an
(b) 16
(a) 8
12
6 5 4 3 2 1 0 -1
VHDA HDA
x-ray S(Q)/ atom
Neutron S(Q) / atom
7
8
VHDA 4
HDA 0
LDA 5 10 15 20 25 -1 Momentum Transfer, Q (Å )
LDA -4 5 10 -1 Momentum Transfer, Q (Å )
15
Fig. 1. Structure-factor data for the three amorphous phases: VHDA, HDA and LDA ice. The neutron diffraction data are shown in (a) and the X-ray data are shown in (b). In both cases, the principal diffraction peak of the VHDA form is observed at a higher Q-value and is sharper than the other amorphous forms.
M. Guthrie et al. / Chemical Physics Letters 397 (2004) 335–339
A portion of the remaining sample (10 mm3) was transferred to the Advance Photon Source at ANL. It was loaded into another helium cryostat situated on the BESSRC 11-ID-C beamline. The temperature of the sample was monitored during the transfer, and was observed to not exceed 77 K. Additionally, the sample was warmed to 80 K to remove excess liquid nitrogen before being cooled back to 40 K for data collection. Angular-dispersive data were collected using a high˚ ). Corrections energy monochromatic X-rays (k = 0.106 A for the variable position of the detector, detector deadtime and background were applied and the data were normalised to the molecular form factor plus Compton scattering. For such high-energy X-ray radiation (115 keV) and small samples, attenuation and multiple-scattering effects are negligible. These X-ray Sx(Q) data are shown in Fig. 1b along with previously collected HDA and LDA ice data [15]. The structure factors in Fig. 1 indicate that the VHDA sample is characterised by a strong diffraction ˚ 1 in the X-ray case and 2.29 (2) peak at 2.30 (2) A 1 ˚ A in the neutron case. Fig. 1 also gives the structure factors for HDA and LDA ice for comparison [14]. Note the increase in the peak position with increasing density, and particularly the increase in the peak height and smaller peak width of the VHDA form relative to the HDA form. The periodicity of the short-intermediate range structure is inversely associated with the position of the principal peak position in S(Q), and its width is often associated with the extent of the ordering. The relative peak width indicates that ordering in the VHDA ice form is likely extended over a significantly longer range than that in the HDA ice form. To develop a more intuitive understanding of the nature of the ordering in VHDA, we have Fourier transformed the data shown in Fig. 1 into radial distribution
(a) 16
functions given as, D(r) = 4pqr(G(r) 1) (where q is the density, and G(r) is the conventional radial distribution function). A Lorch smoothing function was applied in the high Q-region during the transformation of the data to minimize transformation effects in G(r). The neutron and X-ray D(r) functions are shown in Fig. 2a,b, respectively. Also given in both figures are equivalent patterns for LDA and HDA ice determined from the S(Q) functions in Fig. 1. It is clear from both the X-ray and neutron D(r) data that VHDA ice is more highly ordered than both HDA and LDA ice. In VHDA ice at least seven coordination ˚ . While the LDA ice shells are observed out to 20 A ˚, form exhibits noticeable oscillations to roughly 15 A ˚ and in HDA ice it is limited to below 12 A. Furthermore, the almost identical phasing of the higher r data in the X-ray and neutron D(r) functions indicates that this extended ordering is likely associated with oxygen–oxygen correlations. A clear feature corresponding to the hydrogen bonded O O distance is observed in the X-ray data for all three amorphous forms. This is seen at 2.83 (2) ˚ in VHDA ice, which is longer than other amorphous A ˚ in LDA and HDA ice, respecforms (2.75 and 2.80 A tively). The longer value reported here is consistent with the estimate based on Raman measurements of Loerting ˚ in VHDA ice cf. et al. [5]. They reported values of 2.85 A ˚ in HDA ice. However, the measured value re2.81 A ported here is significantly longer then that given by the EPSR results [6], which show clearly a shorter O O distance in VHDA ice relative to the HDA form ˚ in VHDA ice cf. 2.76 A ˚ in HDA ice). (2.69 A Beyond the initial O O peak in the X-ray VHDA ˚ , this data, we also observe clear intensity at 3.39 (4) A has been attributed to the oxygen atom that is observed at slightly longer distances in HDA ice [6]. It seems likely
(b) 24
20 16
3
3
DX(r) (atoms/Å )
12 DN(r) (atoms/Å )
337
8
VHDA
4
HDA
0
LDA
VHDA 12 8 HDA 4 0
-4
LDA
-4 0
5 10 15 Radial Distance, Å
20
0
5
10
15
20
Radial Distance, (Å)
Fig. 2. Neutron (a) and X-ray (b) radial distribution functions, Dn(r) = 4pqr(G(r) 1) for VHDA, HDA and LDA ice. These have been taken by direct Fourier transform of the structure-factor data shown in Fig. 1.
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M. Guthrie et al. / Chemical Physics Letters 397 (2004) 335–339
that in order to accommodate these additional atoms the nearest-neighbour oxygen shell must expand leading to the observed increase in the O O distance in VHDA ice. At still larger distances there is a sharp peak centred ˚ that is not present in the partial rdfs generat 4.97 (3) A ated using the EPSR technique. In the disordered HDA ice data there is a broad band of intensity across this region, but no evidence of a peak. We note that the O–O partial generated in a recent molecular-dynamics simulation [16] closely resembles our measured data. While the authors of this computational work do not comment on its presence, there is a clear peak in the simulated ˚ , i.e., at essentially at the same location data at 5.02 A as the peak we observe. Annealing amorphous ice at pressure and at elevated temperature for longer times may result in a slightly different, and perhaps even more ordered structure, as the glass relaxes to a more stable form. As such, it is instructive to compare the structure of VHDA ice measured here with several dense crystalline phases. For example, in the region 1.0–1.5 GPa, it was found that HDA ice crystallises near 165 K to a mixture of ice VI and ice XII [17]. In order to compare the our measured radial distribution functions with these crystalline phases, radialdistribution functions (consisting of d-functions) for ice VI and ice XII structures were convolved with a ˚ . These Gaussian distribution with a fixed width of 0.2 A data are shown in Fig. 3 along with the HDA and VHDA ice radial-distribution function G(r). The location of the VHDA peaks, and in particular, the emer˚ gence of the peak located at approximately 4.9 A indicates there is at least qualitative resemblance between the short range structure of VHDA and that of
Radial Distribution Function
4
Ice XII 2 Ice VI
VHDA 0 HDA
2
4 6 Radial Distance, r (Å)
the high-pressure crystalline forms synthesized under similar conditions. It is, however, perhaps unreasonable to consider VHDA ice as a nano-crystalline ice form since no crystalline features appear in the measured diffraction pattern. Moreover, several simulations of the powder diffraction pattern of ice VI were conducted using the GSAS suite of crystallographic software [18]. Peak-profile parameters that model the particle-size broadening effects indicate that a particle size of only ˚ still contained clear crystalline features. We thus 20 A conclude that a nano-crystalline terminology is not appropriate in the description of this VHDA ice form studied here. In summary, high-energy synchrotron X-ray and neutron diffraction experiments have been carried out on a VHDA ice sample recovered to ambient pressure. The anomalous height of the principal peak in both diffraction patterns indicates that this VHDA ice is significantly ordered on a short-intermediate length scale and this is measurably different from the HDA and ˚ LDA ice forms. Clear correlations out to at least 20 A are observed in the VHDA ice form, whereas oscillations die out at much shorter distances in unannealed HDA ice radial distribution functions. The presence of these longer range correlations in both X-ray and neutron VHDA D(r) functions identifies them as being most likely due to oxygen–oxygen correlations. Fourier transforms of the X-ray data giving radial distribution functions D(r) = 4pqr(G(r) 1) indicate an increase in the O–O hydrogen bond distance beyond that of HDA ice as additional oxygen atoms are forced into close proximity and accommodated near the first coordination ˚ shell. In addition, a clear coordination shell at 4.97 A is observed in our X-ray measurement, which is has not been previously reported. A direct comparison with the structure of high-pressure liquid water is difficult due to the large temperature difference, however, our comparison of the ordering of VHDA ice and the crystalline phases VI and XII qualitatively suggests a potential relationship between their short range structure in these phases. It is clear that annealing HDA ice under pressure substantially alters the structure by forming a greater degree of intermediate range ordering. Furthermore, we speculate that other annealing temperatures, pressures and time may lead to different levels of ordering in very dense amorphous ice, such that there is no one definitive form. Finally, and perhaps most importantly, this increased intermediate range structure may significantly affect behaviour during the transformation to the low density forms.
8
Fig. 3. The radial-distribution function of HDA and VHDA ice compared with simulated oxygen–oxygen radial distributions for crystalline ice VI, ice XII.
Acknowledgements This work is supported by the Spallation Neutron Source Project (SNS). SNS is managed by UT-Bat-
M. Guthrie et al. / Chemical Physics Letters 397 (2004) 335–339
telle, LLC, under Contract No. DE-AC05-00OR22725 for the US Department of Energy. The US DOE also provided support for measurements at the IPNS and APS Divisions, Argonne National Laboratory under Contract No. W31109ENG 38. In addition the authors acknowledge the help of Mark A. Beno, BESSRC, during the X-ray measurements and the assistance of Jeorg Neuefeind with aspects of the X-ray analysis.
[8] P.H. Poole, F. Sciortino, U. Essman, H.E. Stanley, Nature 360 (1992) 324. [9] O. Mishima, H.E. Stanley, Nature 392 (1998) 164. [10] J. Neuefeind, C.J. Benmore, B. Tomberli, P.A. Egelstaff, J. Phys.: Condens. Matter 14 (2002) L429. [11] In the neutron case, the scattering lengths are obtained from standard tables as bo = 5.803 fm and bd = 6.671 fm partial weighting factors of 8.8% O–O, 49.4% D–D and 41.8% O–D. ˚ 1 The X-ray molecular form-factors have values at Q = 0 A
References [12] [1] O. Mishima, L.D. Calvert, E. Whalley, Nature 310 (1984) 393. [2] D.D. Klug, O. Mishima, E. Whalley, Physica 139 (1986) 475. [3] Y.P. Handa, O. Mishima, E. Whalley, J. Chem. Phys. 84 (1986) 2766. [4] D.D. Klug, Nature 420 (2002) 749. [5] T. Loerting, C. Salzmann, I. Kohl, E. Mayer, A. Hallbrucker, Phys. Chem. Chem. Phys. 3 (2001) 5355. [6] J.L. Finney, D.T. Bowron, A.K. Soper, T. Loerting, E. Mayer, A. Hallbrucker, Phys. Rev. Lett. 89 (2002) 205503. [7] S. Klotz, G. Hamel, J.S. Loveday, R.J. Nelmes, M. Guthrie, A.K. Soper, Phys. Rev. Lett. 89 (2002) 285502.
339
[13] [14] [15] [16] [17] [18]
essentially equal to the number of electrons in each atom with partial weights given as: 64.0% O–O, 4.0% D–D and 32.0% O–D. The Faber–Ziman weighting factors for the X-ray O–D partial decreases much more rapidly than the O–O partial with increasing momentum transfer. J.L. Finney, A. Hallbrucker, I. Kohl, A.K. Soper, D.T. Bowron, Phys. Rev. Lett. 88 (2002) 225503. A.H. Narten, H.A. Levy, J. Chem. Phys. 55 (1971) 2263. P.F. Peterson, M. Gutmann, Th. Proffen, S.J.L. Billinge, J. Appl. Cryst. 38 (2002) 1192. C.A. Tulk, C.J. Benmore, J. Urquidi, D.D. Klug, J. Neuefeind, B. Tomberli, P.A. Egelstaff, Science 297 (2002) 1320. B. Guillot, Y. Guissani, J. Chem. Phys. 119 (2003) 11740. S. Klotz, G. Hamel, J.S. Loveday, R.J. Nelmes, M. Guthrie, Z. Kristallogr. 218 (2003) 117. A.C. Larson, R.B. Von Dreele, Los Alamos National Laboratory, Report LAUR Las Alamos, NM, 2000.
A structural study of very high-density amorphous ice Malcolm Guthrie a
a,b
, Chris A. Tulk
a,*
, Chris J. Benmore b, Dennis D. Klug
c
Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA b Argonne National Laboratory, Argonne, IL 60439, USA c National Research Council of Canada, Ottawa, Ontano, Canada K0A 0R6 Received 8 July 2004 Available online 25 September 2004
Abstract Neutron and X-ray structure factor functions of very high-density amorphous (VHDA) ice have been measured and compared with those of the high- and low-density amorphous forms. The principal peak in the VHDA structure factor is sharper than that ˚ , close to 2.85 A ˚ observed in the HDA ice form. Radial distribution functions (rdfs) indicate the local O O separation is 2.83 A estimated from earlier Raman measurements, but larger than that observed by empirical potential structure refinement simulation of neutron data. Perhaps more importantly the rdfs indicate a greater extent of ordering in VHDA ice, with observable coordination ˚. shells extending to at least 20 A 2004 Elsevier B.V. All rights reserved.
Since the discovery of pressure-amorphised ice 20 years ago [1], the structures of the high-density amorphous (HDA) and low-density amorphous (LDA) ice forms [1–3], and their relation to liquid water have been the subject of intense discussion [4] and by now the basic structural features of each form are well understood. Quite recently however there has been increasing interest in a higher-density form that is synthesized by annealing the HDA form isothermally under pressure [5–7]. Details of the structure of this very high-density form and the relation to HDA and LDA are of current interest, particularly since annealing the amorphous form under pressure is a common practice when forming highdensity pressure amorphized ice and studying the transformation process to the lower density form. Additionally, it has been suggested that the very high-density amorphous (VHDA) ice form may be related to the high-temperature liquid. Understanding the subtle effects of synthesis conditions on the resulting structure may help in understanding the high–low-density amor*
Corresponding author. E-mail address: [email protected] (C.A. Tulk).
0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.07.116
phous ice transformation process. Furthermore, many in situ experiments are preformed at elevated temperatures where the production of this VHDA ice form may be more likely than those formed at liquid nitrogen temperature [4,8,9]. The initial report of the VHDA ice included Raman spectroscopic and some X-ray measurements, but the X-ray data could not be analysed to provide detailed structural information. Subsequently, VHDA ice has been studied using an empirical potential structure refinement (EPSR) technique applied to neutron diffraction data [6]. While these characterisations have shed light onto the structure of VHDA ice, the precise value of the nearest-neighbour O O distance is inconsistent and remains unclear. This may be a result of the weak contribution of the O–O partial to the total neutron S(Q). The Raman data implies a longer bond length than the EPSR simulation. Due to the relative scattering power of waterÕs hydrogen and oxygen atoms the total X-ray structure factor is dominated by the O–O partial [10,11], where as in the case of neutron scattering the O–O partial contributes to less than 9% of the total scattering. This greater
336
M. Guthrie et al. / Chemical Physics Letters 397 (2004) 335–339
sensitivity to the O–O partial is especially important, since it shows the most pronounced differences among the various amorphous ice forms [12,2]. In the work presented here both the neutron and X-ray structure factors S(Q) have been measured, and this data is used to discuss both the local structure and intermediate-range ordering of the VHDA form. We note that, the intermediate-range structure, which may play a significant role in the transformation processes, has not been commented on previously in any great detail. In particular, we compare the VHDA structure to both the lowdensity and high-density structures. The form of the structure factor, S(Q) for both neutron and X-ray diffraction are given below as (the subscript n refers to neutron terms and the subscript x refers to X-ray terms): ( ), !2 X X 2 S n ðQÞ ¼ I n ðQÞ ca ba P ðQÞ c a ba ; a
indium vessel inside a piston-cylinder pressure cell, and cooled to 77 K by immersion in liquid-nitrogen. Both the sample and indium container were then pressurised to 1.8 GPa, followed by depressurization to 1.25 GPa where the sample was warmed from 77 to 165 K, as determined by the average reading of thermocouples attached to the top and bottom of the pressure cell cylinder. These conditions were maintained for 15 min. The sample was then cooled to 77 K and the pressure gradually released to zero. The volume of the sample was estimated from the length of the indium tube at ambient pressure and was found to be 10 ± 2% smaller than the average found for HDA ice prepared in a similar manner, but without the annealing process. The indium canister containing the VHDA sample was recovered under liquid nitrogen, and transferred directly to a storage dewar for shipping to the Argonne National Laboratory (ANL) for the subsequent study. For the neutron scattering experiment the sample was extracted from the indium container and 1 cm3 was placed in a vanadium canister under liquid nitrogen (a smaller amount was kept in reserve, also under liquid nitrogen, for the X-ray measurement). The vanadium canister was then transferred to a continuous-flow Oxford He cryostat mounted in the SEPD instrument at the Intense Pulsed Neutron Source, ANL. The cryostat had been pre-cooled to 40 K and the temperature during the transfer to the cryostat did not exceed 77 K. After the sample loading was complete, the temperature was gradually raised to 80 K to boil off any remaining nitrogen, before being lowered to 40 K and data collected. Standard corrections including subtraction of the container scattering, absorption, multiple-scattering effects and inelastic scattering were implemented using the software package PDFGETN [14]. The resulting neutron Sn(Q) function is shown in Fig. 1a, along with that measured previously from HDA and LDA [15].
a
ð1Þ S x ðQÞ ¼
fI x ðQÞ hF 2 i CðQÞg hF i2
ð2Þ
:
In these equations, I(Q) is the corrected measured intensity. The individual atoms within a given molecule of the sample material are labeled a, and ca represents the fractional proportion of atoms of type a, for neutrons ba are the neutron scattering length of atom type a, and P(Q) is the inelastic (Plazeck) contribution. For X-rays ÆF2æ represents the average scattering from an independent molecule and C(Q) is the Compton scattering contribution [13]. A sample of VHDA ice (99.979% D2O by weight, purchased from Atomic Energy of Canada Ltd.) was prepared at the National Research Council of Canada. Approximately 2.2 cm3 of water were loaded into an
(b) 16
(a) 8
12
6 5 4 3 2 1 0 -1
VHDA HDA
x-ray S(Q)/ atom
Neutron S(Q) / atom
7
8
VHDA 4
HDA 0
LDA 5 10 15 20 25 -1 Momentum Transfer, Q (Å )
LDA -4 5 10 -1 Momentum Transfer, Q (Å )
15
Fig. 1. Structure-factor data for the three amorphous phases: VHDA, HDA and LDA ice. The neutron diffraction data are shown in (a) and the X-ray data are shown in (b). In both cases, the principal diffraction peak of the VHDA form is observed at a higher Q-value and is sharper than the other amorphous forms.
M. Guthrie et al. / Chemical Physics Letters 397 (2004) 335–339
A portion of the remaining sample (10 mm3) was transferred to the Advance Photon Source at ANL. It was loaded into another helium cryostat situated on the BESSRC 11-ID-C beamline. The temperature of the sample was monitored during the transfer, and was observed to not exceed 77 K. Additionally, the sample was warmed to 80 K to remove excess liquid nitrogen before being cooled back to 40 K for data collection. Angular-dispersive data were collected using a high˚ ). Corrections energy monochromatic X-rays (k = 0.106 A for the variable position of the detector, detector deadtime and background were applied and the data were normalised to the molecular form factor plus Compton scattering. For such high-energy X-ray radiation (115 keV) and small samples, attenuation and multiple-scattering effects are negligible. These X-ray Sx(Q) data are shown in Fig. 1b along with previously collected HDA and LDA ice data [15]. The structure factors in Fig. 1 indicate that the VHDA sample is characterised by a strong diffraction ˚ 1 in the X-ray case and 2.29 (2) peak at 2.30 (2) A 1 ˚ A in the neutron case. Fig. 1 also gives the structure factors for HDA and LDA ice for comparison [14]. Note the increase in the peak position with increasing density, and particularly the increase in the peak height and smaller peak width of the VHDA form relative to the HDA form. The periodicity of the short-intermediate range structure is inversely associated with the position of the principal peak position in S(Q), and its width is often associated with the extent of the ordering. The relative peak width indicates that ordering in the VHDA ice form is likely extended over a significantly longer range than that in the HDA ice form. To develop a more intuitive understanding of the nature of the ordering in VHDA, we have Fourier transformed the data shown in Fig. 1 into radial distribution
(a) 16
functions given as, D(r) = 4pqr(G(r) 1) (where q is the density, and G(r) is the conventional radial distribution function). A Lorch smoothing function was applied in the high Q-region during the transformation of the data to minimize transformation effects in G(r). The neutron and X-ray D(r) functions are shown in Fig. 2a,b, respectively. Also given in both figures are equivalent patterns for LDA and HDA ice determined from the S(Q) functions in Fig. 1. It is clear from both the X-ray and neutron D(r) data that VHDA ice is more highly ordered than both HDA and LDA ice. In VHDA ice at least seven coordination ˚ . While the LDA ice shells are observed out to 20 A ˚, form exhibits noticeable oscillations to roughly 15 A ˚ and in HDA ice it is limited to below 12 A. Furthermore, the almost identical phasing of the higher r data in the X-ray and neutron D(r) functions indicates that this extended ordering is likely associated with oxygen–oxygen correlations. A clear feature corresponding to the hydrogen bonded O O distance is observed in the X-ray data for all three amorphous forms. This is seen at 2.83 (2) ˚ in VHDA ice, which is longer than other amorphous A ˚ in LDA and HDA ice, respecforms (2.75 and 2.80 A tively). The longer value reported here is consistent with the estimate based on Raman measurements of Loerting ˚ in VHDA ice cf. et al. [5]. They reported values of 2.85 A ˚ in HDA ice. However, the measured value re2.81 A ported here is significantly longer then that given by the EPSR results [6], which show clearly a shorter O O distance in VHDA ice relative to the HDA form ˚ in VHDA ice cf. 2.76 A ˚ in HDA ice). (2.69 A Beyond the initial O O peak in the X-ray VHDA ˚ , this data, we also observe clear intensity at 3.39 (4) A has been attributed to the oxygen atom that is observed at slightly longer distances in HDA ice [6]. It seems likely
(b) 24
20 16
3
3
DX(r) (atoms/Å )
12 DN(r) (atoms/Å )
337
8
VHDA
4
HDA
0
LDA
VHDA 12 8 HDA 4 0
-4
LDA
-4 0
5 10 15 Radial Distance, Å
20
0
5
10
15
20
Radial Distance, (Å)
Fig. 2. Neutron (a) and X-ray (b) radial distribution functions, Dn(r) = 4pqr(G(r) 1) for VHDA, HDA and LDA ice. These have been taken by direct Fourier transform of the structure-factor data shown in Fig. 1.
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that in order to accommodate these additional atoms the nearest-neighbour oxygen shell must expand leading to the observed increase in the O O distance in VHDA ice. At still larger distances there is a sharp peak centred ˚ that is not present in the partial rdfs generat 4.97 (3) A ated using the EPSR technique. In the disordered HDA ice data there is a broad band of intensity across this region, but no evidence of a peak. We note that the O–O partial generated in a recent molecular-dynamics simulation [16] closely resembles our measured data. While the authors of this computational work do not comment on its presence, there is a clear peak in the simulated ˚ , i.e., at essentially at the same location data at 5.02 A as the peak we observe. Annealing amorphous ice at pressure and at elevated temperature for longer times may result in a slightly different, and perhaps even more ordered structure, as the glass relaxes to a more stable form. As such, it is instructive to compare the structure of VHDA ice measured here with several dense crystalline phases. For example, in the region 1.0–1.5 GPa, it was found that HDA ice crystallises near 165 K to a mixture of ice VI and ice XII [17]. In order to compare the our measured radial distribution functions with these crystalline phases, radialdistribution functions (consisting of d-functions) for ice VI and ice XII structures were convolved with a ˚ . These Gaussian distribution with a fixed width of 0.2 A data are shown in Fig. 3 along with the HDA and VHDA ice radial-distribution function G(r). The location of the VHDA peaks, and in particular, the emer˚ gence of the peak located at approximately 4.9 A indicates there is at least qualitative resemblance between the short range structure of VHDA and that of
Radial Distribution Function
4
Ice XII 2 Ice VI
VHDA 0 HDA
2
4 6 Radial Distance, r (Å)
the high-pressure crystalline forms synthesized under similar conditions. It is, however, perhaps unreasonable to consider VHDA ice as a nano-crystalline ice form since no crystalline features appear in the measured diffraction pattern. Moreover, several simulations of the powder diffraction pattern of ice VI were conducted using the GSAS suite of crystallographic software [18]. Peak-profile parameters that model the particle-size broadening effects indicate that a particle size of only ˚ still contained clear crystalline features. We thus 20 A conclude that a nano-crystalline terminology is not appropriate in the description of this VHDA ice form studied here. In summary, high-energy synchrotron X-ray and neutron diffraction experiments have been carried out on a VHDA ice sample recovered to ambient pressure. The anomalous height of the principal peak in both diffraction patterns indicates that this VHDA ice is significantly ordered on a short-intermediate length scale and this is measurably different from the HDA and ˚ LDA ice forms. Clear correlations out to at least 20 A are observed in the VHDA ice form, whereas oscillations die out at much shorter distances in unannealed HDA ice radial distribution functions. The presence of these longer range correlations in both X-ray and neutron VHDA D(r) functions identifies them as being most likely due to oxygen–oxygen correlations. Fourier transforms of the X-ray data giving radial distribution functions D(r) = 4pqr(G(r) 1) indicate an increase in the O–O hydrogen bond distance beyond that of HDA ice as additional oxygen atoms are forced into close proximity and accommodated near the first coordination ˚ shell. In addition, a clear coordination shell at 4.97 A is observed in our X-ray measurement, which is has not been previously reported. A direct comparison with the structure of high-pressure liquid water is difficult due to the large temperature difference, however, our comparison of the ordering of VHDA ice and the crystalline phases VI and XII qualitatively suggests a potential relationship between their short range structure in these phases. It is clear that annealing HDA ice under pressure substantially alters the structure by forming a greater degree of intermediate range ordering. Furthermore, we speculate that other annealing temperatures, pressures and time may lead to different levels of ordering in very dense amorphous ice, such that there is no one definitive form. Finally, and perhaps most importantly, this increased intermediate range structure may significantly affect behaviour during the transformation to the low density forms.
8
Fig. 3. The radial-distribution function of HDA and VHDA ice compared with simulated oxygen–oxygen radial distributions for crystalline ice VI, ice XII.
Acknowledgements This work is supported by the Spallation Neutron Source Project (SNS). SNS is managed by UT-Bat-
M. Guthrie et al. / Chemical Physics Letters 397 (2004) 335–339
telle, LLC, under Contract No. DE-AC05-00OR22725 for the US Department of Energy. The US DOE also provided support for measurements at the IPNS and APS Divisions, Argonne National Laboratory under Contract No. W31109ENG 38. In addition the authors acknowledge the help of Mark A. Beno, BESSRC, during the X-ray measurements and the assistance of Jeorg Neuefeind with aspects of the X-ray analysis.
[8] P.H. Poole, F. Sciortino, U. Essman, H.E. Stanley, Nature 360 (1992) 324. [9] O. Mishima, H.E. Stanley, Nature 392 (1998) 164. [10] J. Neuefeind, C.J. Benmore, B. Tomberli, P.A. Egelstaff, J. Phys.: Condens. Matter 14 (2002) L429. [11] In the neutron case, the scattering lengths are obtained from standard tables as bo = 5.803 fm and bd = 6.671 fm partial weighting factors of 8.8% O–O, 49.4% D–D and 41.8% O–D. ˚ 1 The X-ray molecular form-factors have values at Q = 0 A
References [12] [1] O. Mishima, L.D. Calvert, E. Whalley, Nature 310 (1984) 393. [2] D.D. Klug, O. Mishima, E. Whalley, Physica 139 (1986) 475. [3] Y.P. Handa, O. Mishima, E. Whalley, J. Chem. Phys. 84 (1986) 2766. [4] D.D. Klug, Nature 420 (2002) 749. [5] T. Loerting, C. Salzmann, I. Kohl, E. Mayer, A. Hallbrucker, Phys. Chem. Chem. Phys. 3 (2001) 5355. [6] J.L. Finney, D.T. Bowron, A.K. Soper, T. Loerting, E. Mayer, A. Hallbrucker, Phys. Rev. Lett. 89 (2002) 205503. [7] S. Klotz, G. Hamel, J.S. Loveday, R.J. Nelmes, M. Guthrie, A.K. Soper, Phys. Rev. Lett. 89 (2002) 285502.
339
[13] [14] [15] [16] [17] [18]
essentially equal to the number of electrons in each atom with partial weights given as: 64.0% O–O, 4.0% D–D and 32.0% O–D. The Faber–Ziman weighting factors for the X-ray O–D partial decreases much more rapidly than the O–O partial with increasing momentum transfer. J.L. Finney, A. Hallbrucker, I. Kohl, A.K. Soper, D.T. Bowron, Phys. Rev. Lett. 88 (2002) 225503. A.H. Narten, H.A. Levy, J. Chem. Phys. 55 (1971) 2263. P.F. Peterson, M. Gutmann, Th. Proffen, S.J.L. Billinge, J. Appl. Cryst. 38 (2002) 1192. C.A. Tulk, C.J. Benmore, J. Urquidi, D.D. Klug, J. Neuefeind, B. Tomberli, P.A. Egelstaff, Science 297 (2002) 1320. B. Guillot, Y. Guissani, J. Chem. Phys. 119 (2003) 11740. S. Klotz, G. Hamel, J.S. Loveday, R.J. Nelmes, M. Guthrie, Z. Kristallogr. 218 (2003) 117. A.C. Larson, R.B. Von Dreele, Los Alamos National Laboratory, Report LAUR Las Alamos, NM, 2000.